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Articles 1 - 11 of 11
Full-Text Articles in Non-linear Dynamics
Symphas: A Modular Api For Phase-Field Modeling Using Compile-Time Symbolic Algebra, Steven A. Silber
Symphas: A Modular Api For Phase-Field Modeling Using Compile-Time Symbolic Algebra, Steven A. Silber
Electronic Thesis and Dissertation Repository
The phase-field method is a common approach to qualitative analysis of phase transitions. It allows visualizing the time evolution of a phase transition, providing valuable insight into the underlying microstructure and the dynamical processes that take place. Although the approach is applied in a diverse range of fields, from metal-forming to cardiac modelling, there are a limited number of software tools available that allow simulating any phase-field problem and that are highly accessible. To address this, a new open source API and software package called SymPhas is developed for simulating phase-field and phase-field crystal in 1-, 2- and 3-dimensions. Phase-field …
Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng
Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng
Theses and Dissertations
Recent numerical work of Carlson-Hudson-Larios leverages a nudging-based algorithm for data assimilation to asymptotically recover viscosity in the 2D Navier-Stokes equations as partial observations on the velocity are received continuously-in-time. This "on-the-fly" algorithm is studied both analytically and numerically for the Lorenz equations in this thesis.
Computational Design Of Nonlinear Stress-Strain Of Isotropic Materials, Askhad M.Polatov, Akhmat M. Ikramov, Daniyarbek Razmukhamedov
Computational Design Of Nonlinear Stress-Strain Of Isotropic Materials, Askhad M.Polatov, Akhmat M. Ikramov, Daniyarbek Razmukhamedov
Chemical Technology, Control and Management
The article deals with the problems of numerical modeling of nonlinear physical processes of the stress-strain state of structural elements. An elastoplastic medium of a homogeneous solid material is investigated. The results of computational experiments on the study of the process of physically nonlinear deformation of isotropic elements of three-dimensional structures with a system of one- and double-periodic spherical cavities under uniaxial compression are presented. The influence and mutual influence of stress concentrators in the form of spherical cavities, vertically located two cavities and a horizontally located system of two cavities on the deformation of the structure are investigated. Numerical …
Lecture 09: Hierarchically Low Rank And Kronecker Methods, Rio Yokota
Lecture 09: Hierarchically Low Rank And Kronecker Methods, Rio Yokota
Mathematical Sciences Spring Lecture Series
Exploiting structures of matrices goes beyond identifying their non-zero patterns. In many cases, dense full-rank matrices have low-rank submatrices that can be exploited to construct fast approximate algorithms. In other cases, dense matrices can be decomposed into Kronecker factors that are much smaller than the original matrix. Sparsity is a consequence of the connectivity of the underlying geometry (mesh, graph, interaction list, etc.), whereas the rank-deficiency of submatrices is closely related to the distance within this underlying geometry. For high dimensional geometry encountered in data science applications, the curse of dimensionality poses a challenge for rank-structured approaches. On the other …
Lecture 07: Nonlinear Preconditioning Methods And Applications, Xiao-Chuan Cai
Lecture 07: Nonlinear Preconditioning Methods And Applications, Xiao-Chuan Cai
Mathematical Sciences Spring Lecture Series
We consider solving system of nonlinear algebraic equations arising from the discretization of partial differential equations. Inexact Newton is a popular technique for such problems. When the nonlinearities in the system are well-balanced, Newton's method works well, but when a small number of nonlinear functions in the system are much more nonlinear than the others, Newton may converge slowly or even stagnate. In such a situation, we introduce some nonlinear preconditioners to balance the nonlinearities in the system. The preconditioners are often constructed using a combination of some domain decomposition methods and nonlinear elimination methods. For the nonlinearly preconditioned problem, …
Lecture 02: Tile Low-Rank Methods And Applications (W/Review), David Keyes
Lecture 02: Tile Low-Rank Methods And Applications (W/Review), David Keyes
Mathematical Sciences Spring Lecture Series
As simulation and analytics enter the exascale era, numerical algorithms, particularly implicit solvers that couple vast numbers of degrees of freedom, must span a widening gap between ambitious applications and austere architectures to support them. We present fifteen universals for researchers in scalable solvers: imperatives from computer architecture that scalable solvers must respect, strategies towards achieving them that are currently well established, and additional strategies currently being developed for an effective and efficient exascale software ecosystem. We consider recent generalizations of what it means to “solve” a computational problem, which suggest that we have often been “oversolving” them at the …
Flocc: From Agent-Based Models To Interactive Simulations On The Web, Scott Donaldson
Flocc: From Agent-Based Models To Interactive Simulations On The Web, Scott Donaldson
Northeast Journal of Complex Systems (NEJCS)
Agent-based modeling (ABM) is a computational technique wherein systems are represented through the actions and interactions of many individual entities (‘agents’) over time. ABM often attempts to elucidate the unpredictable, high-level behavior of systems through the predictable, low-level behavior of actors within the system. There are currently few software or frameworks for ABM that allow modelers to design and build interactive models on the web, for a wide audience as well as a scientifically literate audience well-versed in complexity, models, and simulations. Flocc is a novel framework for agent-based modeling written in JavaScript, the lingua franca programming language of the …
Emergent Hierarchy Through Conductance-Based Degree Constraints, Christopher Tyler Diggans, Jeremie Fish, Erik M. Bollt
Emergent Hierarchy Through Conductance-Based Degree Constraints, Christopher Tyler Diggans, Jeremie Fish, Erik M. Bollt
Northeast Journal of Complex Systems (NEJCS)
The presence of hierarchy in many real-world networks is not yet fully understood. We observe that complex interaction networks are often coarse-grain models of vast modular networks, where tightly connected subgraphs are agglomerated into nodes for simplicity of representation and computational feasibility. The emergence of hierarchy in such growing complex networks may stem from one particular property of these ignored subgraphs: their graph conductance. Being a quantification of the main bottleneck of flow through the coarse-grain node, this scalar quantity implies a structural limitation and supports the consideration of heterogeneous degree constraints. The internal conductance values of the subgraphs are …
Are Terrorist Networks Just Glorified Criminal Cells?, Elie Alhajjar, Ryan Fameli, Shane Warren
Are Terrorist Networks Just Glorified Criminal Cells?, Elie Alhajjar, Ryan Fameli, Shane Warren
Northeast Journal of Complex Systems (NEJCS)
The notions of organized crime and terrorism have an old and rich history around the globe. Researchers and practitioners have been studying events and phenomena related to these notions for a long time. There are pointers in the literature in which it is misleading to see the unfair comparison between terrorist and criminal networks with the argument that all actors involved in these networks are simply evil individuals. In this paper, we conduct a systematic study of the operational structure of such networks from a network science perspective. We highlight some of the major differences between them and support our …
Five-Wave Resonances In Deep Water Gravity Waves: Integrability, Numerical Simulations And Experiments, Dan Lucas, Marc Perlin, Dian-Yong Liu, Shane Walsh, Rossen Ivanov, Miguel D. Bustamante
Five-Wave Resonances In Deep Water Gravity Waves: Integrability, Numerical Simulations And Experiments, Dan Lucas, Marc Perlin, Dian-Yong Liu, Shane Walsh, Rossen Ivanov, Miguel D. Bustamante
Articles
In this work we consider the problem of finding the simplest arrangement of resonant deep water gravity waves in one-dimensional propagation, from three perspectives: Theoretical, numerical and experimental. Theoretically this requires using a normal-form Hamiltonian that focuses on 5-wave resonances. The simplest arrangement is based on a triad of wave vectors K1 + K2 = K3 (satisfying specific ratios) along with their negatives, corresponding to a scenario of encountering wave packets, amenable to experiments and numerical simulations. The normal-form equations for these encountering waves in resonance are shown to be non-integrable, but they admit an integrable reduction …
Modelling The Transition From Homogeneous To Columnar States In Locust Hopper Bands, Miguel Velez
Modelling The Transition From Homogeneous To Columnar States In Locust Hopper Bands, Miguel Velez
HMC Senior Theses
Many biological systems form structured swarms, for instance in locusts, whose swarms are known as hopper bands. There is growing interest in applying mathematical models to understand the emergence and dynamics of these biological and social systems. We model the locusts of a hopper band as point particles interacting through repulsive and attractive social "forces" on a one dimensional periodic domain. The primary goal of this work is to modify this well studied modelling framework to be more biological by restricting repulsion to act locally between near neighbors, while attraction acts globally between all individuals. This is a biologically motivated …